An equation of state for a fluid of fused hard sphere (FHS) molecules is developed based on an interpolation scheme which relates the free energy per particle to that of a fluid of tangent hard sphere (THS) molecules at the same packing fraction. Use of Wertheim’s TPT1 (first order thermodynamic perturbation theory) equation for this latter quantity yields an analytical expression for the compressibility factor for any shape of the FHS molecule. Predictions are in good agreement with the simulation results for rigid homonuclear and heteronuclear diatomics, linear and nonlinear triatomics, and tetrahedral pentatomics. For purely repulsive models of n-alkane chains, it is found that the accuracy of the theory deteriorates with increasing chain length. The interpolation procedure is also generalized to the case of chemical association.